3 * Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
5 * This file is part of FFmpeg.
7 * FFmpeg is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU Lesser General Public
9 * License as published by the Free Software Foundation; either
10 * version 2.1 of the License, or (at your option) any later version.
12 * FFmpeg is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15 * Lesser General Public License for more details.
17 * You should have received a copy of the GNU Lesser General Public
18 * License along with FFmpeg; if not, write to the Free Software
19 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
25 * @author Michael Niedermayer <michaelni@gmx.at>
32 #include "mathematics.h"
35 int av_reduce(int *dst_num, int *dst_den,
36 int64_t num, int64_t den, int64_t max)
38 AVRational a0 = { 0, 1 }, a1 = { 1, 0 };
39 int sign = (num < 0) ^ (den < 0);
40 int64_t gcd = av_gcd(FFABS(num), FFABS(den));
43 num = FFABS(num) / gcd;
44 den = FFABS(den) / gcd;
46 if (num <= max && den <= max) {
47 a1 = (AVRational) { num, den };
52 uint64_t x = num / den;
53 int64_t next_den = num - den * x;
54 int64_t a2n = x * a1.num + a0.num;
55 int64_t a2d = x * a1.den + a0.den;
57 if (a2n > max || a2d > max) {
58 if (a1.num) x = (max - a0.num) / a1.num;
59 if (a1.den) x = FFMIN(x, (max - a0.den) / a1.den);
61 if (den * (2 * x * a1.den + a0.den) > num * a1.den)
62 a1 = (AVRational) { x * a1.num + a0.num, x * a1.den + a0.den };
67 a1 = (AVRational) { a2n, a2d };
71 av_assert2(av_gcd(a1.num, a1.den) <= 1U);
72 av_assert2(a1.num <= max && a1.den <= max);
74 *dst_num = sign ? -a1.num : a1.num;
80 AVRational av_mul_q(AVRational b, AVRational c)
82 av_reduce(&b.num, &b.den,
83 b.num * (int64_t) c.num,
84 b.den * (int64_t) c.den, INT_MAX);
88 AVRational av_div_q(AVRational b, AVRational c)
90 return av_mul_q(b, (AVRational) { c.den, c.num });
93 AVRational av_add_q(AVRational b, AVRational c) {
94 av_reduce(&b.num, &b.den,
95 b.num * (int64_t) c.den +
96 c.num * (int64_t) b.den,
97 b.den * (int64_t) c.den, INT_MAX);
101 AVRational av_sub_q(AVRational b, AVRational c)
103 return av_add_q(b, (AVRational) { -c.num, c.den });
106 AVRational av_d2q(double d, int max)
112 return (AVRational) { 0,0 };
113 if (fabs(d) > INT_MAX + 3LL)
114 return (AVRational) { d < 0 ? -1 : 1, 0 };
116 exponent = FFMAX(exponent-1, 0);
117 den = 1LL << (61 - exponent);
118 // (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64
119 av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max);
120 if ((!a.num || !a.den) && d && max>0 && max<INT_MAX)
121 av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX);
126 int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
128 /* n/d is q, a/b is the median between q1 and q2 */
129 int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
130 int64_t b = 2 * (int64_t)q1.den * q2.den;
132 /* rnd_up(a*d/b) > n => a*d/b > n */
133 int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
135 /* rnd_down(a*d/b) < n => a*d/b < n */
136 int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
138 return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
141 int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
143 int i, nearest_q_idx = 0;
144 for (i = 0; q_list[i].den; i++)
145 if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
148 return nearest_q_idx;
151 uint32_t av_q2intfloat(AVRational q) {
165 if (!q.num && !q.den) return 0xFFC00000;
166 if (!q.num) return 0;
167 if (!q.den) return 0x7F800000 | (q.num & 0x80000000);
169 shift = 23 + av_log2(q.den) - av_log2(q.num);
170 if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);
171 else n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);
173 shift -= n >= (1<<24);
174 shift += n < (1<<23);
176 if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den);
177 else n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift);
179 av_assert1(n < (1<<24));
180 av_assert1(n >= (1<<23));
182 return sign<<31 | (150-shift)<<23 | (n - (1<<23));
193 static const int64_t numlist[] = {
194 INT64_MIN, INT64_MIN+1, INT64_MAX, INT32_MIN, INT32_MAX, 1,0,-1,
195 123456789, INT32_MAX-1, INT32_MAX+1LL, UINT32_MAX-1, UINT32_MAX, UINT32_MAX+1LL
198 for (a.num = -2; a.num <= 2; a.num++) {
199 for (a.den = -2; a.den <= 2; a.den++) {
200 for (b.num = -2; b.num <= 2; b.num++) {
201 for (b.den = -2; b.den <= 2; b.den++) {
202 int c = av_cmp_q(a,b);
203 double d = av_q2d(a) == av_q2d(b) ?
204 0 : (av_q2d(a) - av_q2d(b));
206 else if (d < 0) d = -1;
207 else if (d != d) d = INT_MIN;
209 av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num,
210 a.den, b.num, b.den, c,d);
211 r = av_sub_q(av_add_q(b,a), b);
212 if(b.den && (r.num*a.den != a.num*r.den || !r.num != !a.num || !r.den != !a.den))
213 av_log(NULL, AV_LOG_ERROR, "%d/%d ", r.num, r.den);
219 for (i = 0; i < FF_ARRAY_ELEMS(numlist); i++) {
220 int64_t a = numlist[i];
222 for (j = 0; j < FF_ARRAY_ELEMS(numlist); j++) {
223 int64_t b = numlist[j];
226 for (k = 0; k < FF_ARRAY_ELEMS(numlist); k++) {
227 int64_t c = numlist[k];
233 res = av_rescale_rnd(a,b,c, AV_ROUND_ZERO);
235 ai = av_mul_i(av_int2i(a), av_int2i(b));
236 ai = av_div_i(ai, av_int2i(c));
238 if (av_cmp_i(ai, av_int2i(INT64_MAX)) > 0 && res == INT64_MIN)
240 if (av_cmp_i(ai, av_int2i(INT64_MIN)) < 0 && res == INT64_MIN)
242 if (av_cmp_i(ai, av_int2i(res)) == 0)
245 // Special exception for INT64_MIN, remove this in case INT64_MIN is handled without off by 1 error
246 if (av_cmp_i(ai, av_int2i(res-1)) == 0 && a == INT64_MIN)
249 av_log(NULL, AV_LOG_ERROR, "%"PRId64" * %"PRId64" / %"PRId64" = %"PRId64" or %"PRId64"\n", a,b,c, res, av_i2int(ai));
254 for (a.num = 1; a.num <= 10; a.num++) {
255 for (a.den = 1; a.den <= 10; a.den++) {
256 if (av_gcd(a.num, a.den) > 1)
258 for (b.num = 1; b.num <= 10; b.num++) {
259 for (b.den = 1; b.den <= 10; b.den++) {
261 if (av_gcd(b.num, b.den) > 1)
263 if (av_cmp_q(b, a) < 0)
265 for (start = 0; start < 10 ; start++) {
269 for (i = 0; i<100; i++) {
270 int exact = start + av_rescale_q(i+1, b, a);
271 acc = av_add_stable(a, acc, b, 1);
272 if (FFABS(acc - exact) > 2) {
273 av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %d\n", a.num,
274 a.den, b.num, b.den, acc, exact);
284 for (a.den = 1; a.den < 0x100000000U/3; a.den*=3) {
285 for (a.num = -1; a.num < (1<<27); a.num += 1 + a.num/100) {
286 float f = av_int2float(av_q2intfloat(a));
287 float f2 = av_q2d(a);
288 if (fabs(f - f2) > fabs(f)/5000000) {
289 av_log(NULL, AV_LOG_ERROR, "%d/%d %f %f\n", a.num,